Distributed Adaptive Control for Constrained Nash Equilibrium Seeking With Delays

Abstract

This letter addresses distributed Nash equilibrium (NE) seeking for a class of nonlinear Euler–Lagrange multi-agent systems subject to separable coupling constraints and constant communication delays. Each agent aims to regulate its output to the NE of a virtual static game while exchanging delayed information and operating under unknown dynamics and bounded disturbances. To this end, we introduce a set of delay-aware error variables embedding the gradients of the local cost and constraint functions. A distributed adaptive control law, combined with primal–dual projected dynamics, is designed to drive these errors to zero despite communication delays. Sufficient conditions on the controller gains and the delay magnitude are derived to guarantee asymptotic convergence to the unique NE. The effectiveness of the proposed framework is illustrated through simulations involving a network of nonholonomic mobile robots.